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Browsing Department of Mathematics & Statistics by Title

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  • Butler, Steve; Catral, Minnie; Fallat, Shaun; Hall, Tracy; Hogben, Leslie; van den Driessche, Pauline; Young, michael (Elsevier, 2015)
    The enhanced principal rank characteristic sequence (epr-sequence) of a symmetric n ×n matrix is a sequence from A,S, or N according as all, some, or none of its principal minors of order k are nonzero. Such sequences give ...
  • Guo, Chun-Hua; Higham, Nicholas J.; Tisseur, Francoise (SIAM, 2009)
    A 25-year old and somewhat neglected algorithm of Crawford and Moon attempts to determine whether a given Hermitian matrix pair $(A,B)$ is definite by exploring the range of the function $f(x) = x^*(A + iB)x/|x^*(A + ...
  • Borg, Peter; Meagher, Karen (2014-01-21)
  • Guo, Chun-Hua (Taylor & Francis, 2013)
    We start with a discussion of coupled algebraic Riccati equations arising in the study of linear-quadratic optimal control problem for Markov jump linear systems. Under suitable assumptions, this system of equations has ...
  • Guo, Chun-Hua; Lin, Wen-Wei (SIAM, 2010)
    The matrix equation $X+A^TX^{-1}A=Q$ has been studied extensively when $A$ and $Q$ are real square matrices and $Q$ is symmetric positive definite. The equation has positive definite solutions under suitable conditions, ...
  • Barrett, Wayne; Butler, Steve; Catral, Minnie; Hall, Tracy; Fallat, Shaun; Hogben, Leslie; Young, Michael (International Linear Algebra Society, 2014-06)
    Barrett et al. asked in [W. Barrett et al. Minimum rank of edge subdivisions of graphs. Electronic Journal of Linear Algebra, 18:530–563, 2009.], whether the maximum nullity is equal to the zero forcing number for all ...
  • Ahmadi, Bahman; Alinaghipour, Fatemeh; Cavers, Michael; Fallat, Shaun; Meagher, Karen; Nasserasr, Shahla (International Linear Algebra Society, 2013-09)
    The minimum number of distinct eigenvalues, taken over all real symmetric matrices compatible with a given graph G, is denoted by q(G). Using other parameters related to G, bounds for q(G) are proven and then applied to ...
  • Guo, Chun-Hua (Springer, 2013)
    For the algebraic Riccati equation whose four coefficient matrices form a nonsingular $M$-matrix or an irreducible singular $M$-matrix $K$, the minimal nonnegative solution can be found by Newton's method and the doubling ...
  • Barrett, Wayne; Fallat, Shaun; Hall, Tracy; Hogben, Leslie (Public Knowledge Network, 2013)
    We establish the bounds 4 on the Nordhaus- Gaddum sum upper bound multipliers for all graphs G, in connections with certain Colin de Verdi ere type graph parameters. The Nordhaus-Gaddum sum lower bound is conjectured ...
  • Fital, Sandra; Guo, Chun-Hua (Elsevier, 2008)
    The fixed-point iteration is a simple method for finding the maximal Hermitian positive definite solutions of the matrix equations $X\pm A^*X^{-1}A=I$ (the plus/minus equations). The convergence of this method ...
  • Guo, Chun-Hua; Kuo, Yueh-Cheng; Lin, Wen-Wei (Elsevier, 2012)
    The Green's function approach for treating quantum transport in nano devices requires the solution of nonlinear matrix equations of the form $X+(C^*+{\rm i} \eta D^*)X^{-1}(C+{\rm i} \eta D)=R+{\rm i}\eta P$, where $R$ ...
  • Guo, Chun-Hua (Elsevier, 2013)
    We consider the algebraic Riccati equation for which the four coefficient matrices form an $M$-matrix $K$. When $K$ is a nonsingular $M$-matrix or an irreducible singular $M$-matrix, the Riccati equation is known to have ...
  • Guo, Chun-Hua; Kuo, Yueh-Cheng; Lin, Wen-Wei (SIAM, 2012)
    The matrix equation $X+A^{T}X^{-1}A=Q$ arises in Green's function calculations in nano research, where $A$ is a real square matrix and $Q$ is a real symmetric matrix dependent on a parameter and is usually indefinite. ...
  • Guo, Chun-Hua (Elsevier, 2010)
    If $A$ is a matrix with no negative real eigenvalues and all zero eigenvalues of $A$ are semisimple, the principal $p$th root of $A$ can be computed by Newton's method or Halley's method, with a preprocessing procedure ...
  • Meagher, Karen; Fallat, Shaun; Yang, Boting (Elsevier, 2015)
    The positive semidefinite zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring and is related to a more conventional version of zero forcing. We establish a relation ...
  • Fallat, Shaun; Nasserasr, Shahla (The Charles Babbage Research Centre, 2013-02)
    In this work, we study the structure of the null spaces of matrices associated with graphs. Our primary tool is utilizing Schur complements based on certain collections of independent vertices. This idea is applied in ...
  • Alinaghipour, Fatemeh; Fallat, Shaun; Meagher, Karen (2014)
    The zero forcing number and the positive zero forcing number of a graph are two graph parameters that arise from two types of graph colourings. The zero forcing number is an upper bound on the minimum number of induced ...
  • Barioli, Francesco; Barrett, Wayne; Fallat, Shaun; Hall, Tracy; Hogben, Leslie; Shader, Bryan; van den Driessche, Pauline; van der Holst, Hein (Wiley Periodicals, Inc., 2013)
    Tree-width, and variants that restrict the allowable tree decompositions, play an important role in the study of graph algorithms and have application to computer science. The zero forcing number is used to study the ...
  • Guo, Chun-Hua; Liu, Changli; Xue, Jungong (Oxford University Press, 2014)
    A new class of complex nonsymmetric algebraic Riccati equations has been studied by Liu and Xue (SIAM J. Matrix Anal. Appl., 33 (2012), 569-596), which is related to the M-matrix algebraic Riccati equations. Doubling ...
  • Barrett, Wayne; Butler, Steve; Catral, Minnie; Fallat, Shaun; Hall, Tracy; Hogben, Leslie; van den Driessche, Pauline; Young, Michael (Elsevier, 2014)
    Given an n-by-n matrix, its principal rank characteristic sequence is a sequence of length n + 1 of 0s and 1s where, for k = 0; 1,..., n, a 1 in the kth position indicates the existence of a principal submatrix of rank ...

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